CO oxidation on Pt nanoclusters of approximately 1 nm in size was studied using density functional theory (DFT). Reaction barriers on various sites of a cuboctahedral 55-atom cluster and of several two-layer plane clusters representing (111) and (100) facets of the 147-atom cluster have been calculated at various coverage. The effect of atomic structure of various clusters was discussed. It was concluded that the 147-atom cuboctahedral cluster reveals properties of the Pt single crystal surfaces, while a 55-atom cluster cannot be fully described in terms of Pt single crystal surfaces. It was found that CO oxidation may occur faster at higher coverage and that for cluster sizes up to a few nanometers in size, larger platinum clusters can be more efficient in CO oxidation than the smaller clusters. The size effect was found to depend upon coverage.